Let f:(0,∞)R be given by f(x)=∫x1xte−(t+t1)dt, then (a)f(x) is monotonically increasing on [1,∞)(b)f(x) is monotonically decreasing on (0,1)(c)f(2x) is an odd function of x on R

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Let {f}:{({0},)}{{R}} be given by {f{{({x})}}}={_{{{{1}}{{x}}}

Question

Let $f : (0, \infty) R$ be given by $f (x) = \int_{\frac{1}{x}}^{x} \frac{e ^{- (t + \frac{1}{t})} d t}{t},$ then (a) $f (x)$ is monotonically increasing on $[1, \infty)$ (b) $f (x)$ is monotonically decreasing on $(0, 1)$ (c) $f (2^{x})$ is an odd function of $x$ on $R$

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Sofia Discussed

Let

f : (0, \infty) R

be given by

f (x) = \int_{\frac{1}{x}}^{x} \frac{e ^{- (t + \frac{1}{t})} d t}{t},

then (a)

f (x)

is monotonically increasing on

[1, \infty)

(b)

f (x)

is monotonically decreasing on

(0, 1)

(c)

f (2^{x})

is an odd function of

x

R

12 mins ago

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